Sports fans all over the world have recently witnessed an
increasing number of spectacular doping cases, leading to considerable
annoyance in the public. However, our knowledge regarding the prevalence
of doping is still quite limited, leading some people to speculate that
(nearly) all professional athletes are doped and possibly even have to
be doped to be good enough to compete successfully in highly selective
tournaments. On the other hand, particularly representatives of the
sports associations pretend that since the number of positively tested
athletes remains small, there are only a few "black sheep,"
while in general, the world of sport is clean and fair. In the recent
past, a number of theoretical models have been developed that can be
empirically tested, which, in the end, may lead to the formulation of
policy recommendations (ranging from higher sanctions to legalizing
doping). We review the more important models and present anecdotal as
well as some quantitative empirical evidence on the prevalence as well
as the determinants of doping. (JEL K42, L83, M52)

1.INTRODUCTION

It is commonly acknowledged that rankorder tournaments not only
have desirable features--such as inducing high effort levels among
participants--but also share characteristics that can be quite
problematic: the more skewed the structure of the rewards is, the more
incentives the contestants have to engage in activities that are not in
the interest of the organizer (Lazear and Rosen, 1981; Nalebuff and
Stiglitz, 1983; O'Keefe, Viscusi, and Zeckhauser, 1984). Examples
of such activities include plagiarism and manipulation of research
results by academics, fraudulent accounting by managers, mobbing and
sabotage by "normal" employees competing for a promotion, and
the use of steroids and other performance-enhancing drugs by
professional athletes. What all these situations have in common is that
a number of individuals compete for a given winner prize (be it a
tenure-track position, a significant pay increase, an appointment to an
attractive position, or a gold medal). Moreover, in each of these
situations, the contestants usually have the opportunity of increasing
their individual success probabilities by developing activities that are
illegal and, therefore, unacceptable. The economic consequences of these
kinds of behavior can be quite significant as it will very often lead
not only to a misallocation of talent but also to a decrease in
incentives, given that contestants can observe the
"cheating"1.

Since individual athletes can improve their probability of winning
not only by the right kind of training but also by using banned or
illicit substances that enhance performance, it is difficult to
distinguish between performance that is to be attributed to talent and
hard work and performance that is due to illegal preparation, that is,
doping (cf. Preston and Szymanski, 2003, pp. 612-613). Assuming that
event organizers as well as spectators have a preference for
"clean" athletes,(2) separating the two sources of performance
is crucial for obvious reasons: as can be currently seen in one of the
most doping-prone disciplines--professional cycling--sponsors as well as
fans seem to be disgusted by the behavior of many (possibly even most)
riders.(3) While the former reduce their financial support or withdraw
completely from the sport (like the owner of the Swiss top team
"Phonak"), the latter increasingly refuse to watch the races
either live or on television (during the recent 2006 Tour de France--the
most prestigious multistage race--TV ratings plummeted to a record low
in most European countries).

After a brief review of the history of doping methods and scandals
(Section II), the article proceeds as follows: in Section III, we
compare different microeconomic approaches to modeling the behavior of
rational athletes; Section IV presents some empirical evidence
consistent with the theoretical reasoning; and Section V concludes.

II. THE HISTORY OF DOPING METHODS AND SCANDALS

A. Past and Recent Doping Methods

The term "doping" is commonly used to describe the
nontherapeutic use of legal substances (like caffeine(4)), illegal ones
(like cocaine), and drugs (like erythropoietin [EPO]) to improve
athletic performance. Doping is, therefore, a particular form of
"cheating," that is, the intentional and deliberate violation
of implicit or explicit rules to create an "unfair" advantage
in one's own interest and at the expense of others.

Doping is certainly not a recent phenomenon: Greek wrestlers and
Roman gladiators tried to improve their physical strength by eating
sheep's testicles. As early as the late 19th century, professional
cyclists were using substances like caffeine and cocaine to improve
their performance, reduce pain, and delay fatigue. In the early 20th
century, heroine and cocaine were used widely by professional athletes
until they became available only on prescription. In the 1930s,
amphetamines replaced strychnine, a drug that, in combination with
brandy, had nearly killed Olympic marathon runner Thomas Hicks in 1904.
In the 1950s, Soviet athletes started to use male hormones, with the
Americans following soon with steroids. More recently, anabolic steroids
(e.g., used by many baseball players as well as by track and field
athletes) have been replaced by "blood doping," especially
with EPO, as the most prominent way of "artificially"
improving athletes' performance (cf. Wagner, 2000).

Testing for illegal substances has become a "big
business," with athletes trying to hide or mask their use from
officials, fans, and fellow competitors, while laboratories are
developing additional and more sensitive procedures, allowing to detect
even small residues of illegal drugs and substances. Thus, detecting
drug use and evading detection have become a contest in itself, leading
to a specific form of an "arms race": since in the meantime it
can even be determined if the body's hemoglobin level has been
influenced by blood doping, athletes have recently switched from using
normal therapeutic doses to "rnicrodosing," which means that
substance use can be detected only within a very short period of time.
Moreover, athletes can apparently mask substance use by introducing
protease enzymes, for example, that destroy traces of EPO in human urine
(cf. Schmidt et al., 2000).

B. A Selective Survey of Recent Drug Scandals

Since doping has always been and continues to be particularly
prevalent in cycling and track and field, we restrict ourselves here to
the most prominent offenders from these two sports that attract
particularly large numbers of spectators and large amounts of money from
sponsors and TV stations. (5) Before presenting some systematic evidence
on the doping behavior of athletes (see Section IV), we list a number of
spectacular cases that occurred in the recent past in these two sports.

Cycling.

* During the 1967 Tour de France, British rider Tom Simpson
collapsed during the ascent of the Mont Ventoux. Despite immediate
medical treatment, Simpson died. Two tubes of amphetamines were found in
the rear pocket of his racing jersey.

* In 1998, the entire Festina team was excluded from the Tour de
France following the discovery of a team car with large amounts of
various performance-enhancing drugs. The team director later admitted
that some of the cyclists were routinely given banned substances.

* More recently, David Millar, the 2003 World-Time Trial Champion,
admitted using EPO. He lost his title and was suspended for 2 yr. Still
later, Roberto Heras was stripped of his victory in the 2005 Vuelta a
Espana and suspended for 2 yr after testing positive for EPO.

* In 2006, Spanish police arrested five people, including the
sporting director of the Liberty Seguros cycling team, on charges of
running a massive doping scheme involving most of the team and many
other top cyclists. Several potential contenders in the 2006 Tour de
France, such as Jan Ulrich, Ivan Basso, and Oscar Sevilla, were forced
to withdraw.

* Less than a week after the 2006 Tour de France, it was revealed
that winner Floyd Landis had tested positive for an elevated
testosterone-to-epitestosterone ratio after his stunning victory on
Stage 17. A second test confirmed the preliminary findings of deficient
levels of epitestosterone. A decision to strip Landis of the title is
still pending.

* In September 2006, some former teammates of Lance Armstrong
admitted that they had taken EPO during the 1999 Tour de France. While
they did not state that Armstrong had done the same, the press attacked
Armstrong, who throughout his career had been a target of doping
allegations.

Among the 20 teams that are currently admitted to the "Pro
Tour," the highest league in professional cycling, 9 are managed by
former riders who have been found guilty of doping (AG2R Prevoyance,
Astana, Discovery Channel, Gerolsteiner, Quick Step, Rabobank, T-Mobile,
CSC, and Credit Agricole). In the years 1940-2005, about 600 different
riders have been found cheating, among them some 75 individuals who have
been tested positively more than once (http://www.cycling4fans. com).

Track and Field.

* During the 1970s and 1980s, many athletes from Eastern bloc
nations were suspected of augmenting their ability with some kind of
pharmacological help (some of the world records in the track and field
disciplines are now more than 20 yr old). After the fall of communism in
Eastern Europe and the reunification of Germany, documents surfaced,
proving that the East German sport establishment had conducted
systematic doping of virtually all its world-class athletes.

* Canadian sprinter Ben Johnson failed the drug test when anabolic
steroids were found in his urine after his victory in the 100 m at the
1988 Summer Olympics. He later admitted to have taken other drugs and
human growth hormones as well. Carl Lewis was promoted one place to take
the Olympic gold medal. Later, it was revealed that he also had been
using drugs.

* 100 m world champion Katrin Krabbe was found guilty of having
used anabolic steroids in 1992 at least two times.

* At the Olympic Games 2004 in Athens, Greek sprinters Kostas
Kenteris and Ekaterini Thanou feigned a motorcycle accident to avoid a
doping test. The Hungarian hammer thrower Adrian Annus was deprived of
the gold medal because he manipulated his first doping test and refused
a second one. The Hungarian discus thrower Robert Fazekas lost his gold
medal after avoiding a first doping test and trying to swap the urine
sample in the second one.

* In July 2005, the founders of "Bay Area Laboratory
Co-operative," based in California, admitted the production and
distribution of anabolic steroids. Those implicated or accused in the
ensuing scandal included track and field athletes Dwain Chambers, C. J.
Hunter, Marion Jones, and Tim Montgomery.(6)

Much of the (economics) literature on the use of drugs in sport is,
at best, based on anecdotal evidence. The lack of rigorous evidence,
however, is not surprising as athletes taking substances know that they
are doing something that is taboo, illegal, and sometimes highly
dangerous. Nevertheless, the rewards to winning combined with the
increasing effectiveness of the available drugs and the consistently low
rate of detection create a "cheating game" that could be
irresistible to most (professional) athletes as the next section of our
article shows.

III. A REVIEW OF THE THEORETICAL LITERATURE

There are currently four different, though closely related, topics
in the economic analysis of doping. First, some authors still try to
find a convincing definition of the term (see above) by distinguishing
it from other (legal) activities such as training at high altitude and
specific diets. Second, there is much interest in the incentives that
lead athletes to use illegal substances. This leads to the third (and
most pertinent) question: how can these incentives be altered; which
factors advance, and which ones prevent doping? Fourth, it is worth
analyzing why doping is strictly forbidden and whether it is possible or
desirable to stop athletes using illicit medication. Most economists are
interested in the second and third questions only as they have some
expertise analyzing incentives and the ways these have to be designed to
elicit the desired behaviors.(7) However, all the four issues are
closely related: it is certainly difficult to explain why athletes are
doping and how such behaviors can be prevented without some convincing
definition of the term doping. Conversely, if doping only means
consumption of illicit medication, then the abolition of these rules
would solve all doping problems by definition.

Breivik (1987) is the first to characterize the doping problem as a
potential prisoners' dilemma.(8) Doping by one athlete raises his
probability of winning, whereas doping by other athletes decreases that
probability. If all athletes use illicit medication, their individual
probabilities of winning are more or less the same compared with a
situation where everybody refuses to take performance-enhancing drugs.
But in case they all dope, all have to bear the costs of doping. These
costs include all discounted future health problems generated by
doping.(9) However, most athletes do not care much about these costs
because of a high preference for the present and also a very strong
preference for winning (Bird and Wagner, 1997). Haugen (2004, p. 68)
cited Andrews (1998) who reported findings initially presented by sports
journalist Bob Goldman: more than half of 198 U.S. top athletes admitted
that they would take drugs if that made them a winner for 5 yr without
being detected even if they certainly died after these 5 yr due to the
side effects of doping (without these side effects, only two declined to
take such hypothetical drugs). Other costs of doping are the procurement
costs, the moral costs of norm infringement, and, last but not the
least, the expected costs of detection and punishment. In a world
without a ban on doping and, therefore, without this last kind of cost
(and perhaps also without moral costs), doping would possibly be a
dominant strategy for all athletes (Daumann, 2003). This, in turn,
implies the existence of a prisoners' dilemma because all athletes
have to bear the remaining costs of doping without changing their
individual win probabilities. Even if the tournament setting is a
repeated prisoners' dilemma, this is unlikely to result in a
doping-free world because the individuals' incentives not to cheat
are weak and the existence of end-game effects guarantees that at least
some athletes will continue doping.

It follows that an external institution is required to prevent
doping by closely monitoring athletes and by punishing those who are
detected. Even without direct punishment of doping offenders, such an
institution could improve the conditions for collusion among the
athletes, for example, by requiring athletes to keep a "drug
diary" in which they have to include all the (legal and illegal)
substances they are using (this instrument was first proposed by Keck
and Wagner [1990] and Wagner [1994]). Nevertheless, even with a drug
diary, some punishment is required if an athlete is found guilty of
having consumed a drug not included in his/her diary. Bird and Wagner
(1997, p. 759), therefore, suggested the introduction of a "peer
monitoring system," where any two athletes may accuse a third one
of not having listed all the drugs he/she had been using recently. The
accused athlete will then be tested accordingly. In order to avoid false
accusations, the two whistleblowers will be punished if the accused
athlete is found not guilty. A further possible solution of the doping
problem would of course be a reduction of the incentives to win by
lowering the prize money that is at stake in a particular competition.
The obvious disadvantage of such a strategy is that it not only reduces
the incentive to dope but also and primarily the incentives to train and
to pursue an athletic career. Therefore, the costs of doping should be
increased by punishing any athlete who is found guilty of having used
medication that is included in a "negative list" of illicit
substances and procedures.(10) This list, in turn, should be updated
constantly by offering bonus payments to anyone who develops and/or
brings to the sporting associations' attention new drugs that
significantly and measurably enhance the individual's performance.
Such innovation bonuses are likely to reduce the monopoly rents of
innovators of new drugs and--indirectly--the incentive to search for
such innovations in the first place (Daumann, 2003).

Haugen (2004) also interpreted doping as a binary choice variable
in a prisoners' dilemma framework. In the simple case of two
equally talented and trained athletes and a winner's prize a, both
athletes receive an expected value of 1/2a if they refrain from doping.
If one athlete dopes, he is detected with probability r and has in this
case to incur costs c, implying expected costs of doping re. However, if
only one athlete dopes while the other does not, the former wins with
certainty and gets a - re in total, whereas the clean athlete gets
nothing.(11) Finally, if both athletes are doped, their individual
success probabilities are 1/2 again, but both have to bear the expected
cost of rc, (12) resulting in expected benefits of 1/2a-rc for each of
them. This is lower than 1/2a, implying that doping is inefficient.
Nevertheless, doping is the dominant strategy for both athletes as long
as 1/2 a [greater than] re. Given the high prize money a and the low
detection probability r, this is probably true in most professional
sports today (but the symmetry of the athletes involved may be lacking).

The game-theoretical model of Berentsen (2002, p. 110) is more
sophisticated.(13) He also analyzed the case of two athletes who
"simultaneously and secretly decide to use a performance-enhancing
drug before competing." However, this does not necessarily imply
the existence of a prisoners' dilemma because doping is not a
dominant strategy for heterogeneous players, which, in turn, improves
the possibilities to prevent doping. Berentsen (2002, p. lll) made a
strong case for doping prevention by arguing that it never increases
overall welfare. Moreover, "the'wrong'player [the one
with less talent] may win the game because doping changes the
probabilities of winning." A particular problem that deserves
special attention is "that doping tests sometimes provide faulty
information. Occasionally, tests indicate that the athlete is not doped
when he or she is or that an athlete is doped when he or she is
not" (Berentsen, 2002, p. 111). This, in turn, is a strong argument
against the simple advice that by raising sanctions, the extent of
doping could be reduced.

Although the model developed by Berentsen (2002) is quite complex,
its intuition is straightforward. He first defined "a critical
value [tilde.C]" as the ratio of the costs of doping c and the
(higher) value of winning a. This is compared to [[delta].sub.1]],
defined as "the effectiveness of performance-enhancing drugs in the
sense of measuring the increase of player s winning probability when
only player i dopes" (Berentsen, 2002, p. 112). Without doping,
Player 1 may be at least as good as Player 2, implying that his
individual win probability is at least .5. If he dopes and Player 2 does
not, this probability raises by [[delta].sub.1]. Conversely, the win
probability of Player 2 rises by [[delta].sub.2] if he alone dopes.
Moreover, Berentsen (2002, p. 112) assumed "that
performance-enhancing drugs are more effective for the weak player,
i.e., that [[delta].sub.2] [greater than or equal to]
[[delta].sub.1]," which holds even if the physical performance of
both athletes is improved to the same extent.

If [[delta].sub.1]]>[tilde.c], doping is cost-effective (too
cheap relative to its effectiveness) and both athletes will dope with
certainty. If, however, [[delta].sub.2]] < [tilde.c], doping does not
pay and both athletes will remain clean. If [[delta].sub.1] = [tilde.c],
either both athletes may dope or only Athlete 1 may do so. If
[[delta].sub.2] = [tilde.c], both athletes may abstain from doping or
only Athlete I does, whereas Athlete 2 dopes. If [[delta].sub.1] =
[[delta].sub.2] = [tilde.c], all four variants so far are possible
equilibria. Most interesting, however, is the remaining case where
[[delta].sub.1].>[tilde.c]>[[delta].sub.1]] because it represents
a mixed strategy equilibrium. Here, Athlete I dopes with probability
[alpha] = ([[delta].sub.2]-[tilde.c])/([[delta].sub.2]-[[delta].sub.1]
and Athlete 2 with probability [beta] =
([tilde.c]-[[delta].sub.1]/([[delta].sub.2]-[[delta].sub.1]). Athlete 1
dopes with a higher probability than Athlete 2 ([alpha] > [beta]) if
the performance-enhancing drugs are sufficiently effective, that is, if
[[delta].sub.1]+[[delta].sub.2] > 2[tilde.c]. Who of the two athletes
wins with a higher probability also depends on the parameter values: if
[square root of ([[delta].sub.1][[delta].sub.2])] < [tilde.c], the
more talented player (Athlete 1) is less likely to win with doping
opportunities than without. If both conditions are combined, the
favorite is more likely to use performance-enhancing drugs than the
underdog; yet, he is less likely to win with doping opportunities than
without (Berentsen, 2002, p. 113), a result that is counterintuitive.
(14)

Moreover, Berentsen (2002) found a nonmonotonic response to
sanctions for defaulted dopers. Whereas other authors recommended
increasing sanctions as a panacea against doping without further
qualification, Berentsen showed that this holds only for very high
sanctions: there is always a level of sanctions S that deters from
doping, but this level can be extremely high,, especially if the
incentive to win a is large. One may indeed be tempted to support the
idea of very high sanctions for doped athletes, but as long as there are
wrongly positive test results for clean athletes with probability
[[theta][sub.nd], sanctions can be too high and can violate the
participation constraint such that talented athletes refuse not only to
dope but also to enter the competition.

Below this doping-preventing threshold, higher sanctions can even
raise instead of reduce the probability of doping, especially for the
less talented Athlete 2. With some restrictions on the parameter space
of the general model, the following holds: without any sanctions or
s:=,S/a below a threshold [[sigma].sub.1], both athletes dope with
certainty. With s ranging between [[signma].sub.1] and [[sigma].sub.2]
the better Athlete 1 dopes with certainty and the less gifted Athlete 2
refuses to dope. For [[sigma].sub.1]] < s < [[eta[sub.3], there
are mixed equilibria in which both athletes are doping with some
probability that is decreasing in s for Athlete 1 and increasing in s
for Athlete 2. If [[sigma].sub.3]] < s < [[eta[sub.4], Athlete 2
dopes with certainty, while Athlete 1 refuses to dope. Finally, only s
> [[alpha].sub.4] guarantees a sport that is free of doping, [alpha]
is rising in the effectiveness of doping 6 and decreasing in the quality
of the test technology, that is, the probability [[theta].sub.d] by
which a doped athlete can actually be identified. Interestingly, a
higher p, the win probability of Athlete 1 in case nobody is doping,
leads to additional mixed equilibria because it lowers [[alpha].sub.1]
and [[alpha].sub.2] while raising [[alpha].sub.3] and [[alpha].sub.4].

Moreover, Berentsen (2002) showed that an identical level of
sanctions S for a positively tested winner and the loser of a contest is
not adequate. For some specific parameter constellations, identical
sanctions can either not prevent doping or violate the participation
constraint of the weaker Athlete 2. In the model, the ranking-based
punishment scheme [s.sub.1] = (1-[[theta].sub.d] - [[theta].sub.nd] +
[[theta].sub.nd.sup.2] - [[tilde].c])/[[theta].sub.d] and [s.sub.2] = 0
is a perfect mechanism (Berentsen, 2002, p. 113), where [S.sub.1] =
[s.sub.1] a is the sanction for the winner if he or she is positively
tested and [S sub 2] = [s sub 2] a is the sanction for the loser if
positively tested. The recommendation therefore is to treat winners and
losers differently and to probably abandon punishments and doping tests
for the losers. Even if the tests have to be performed before the winner
has been identified, it is possible to prevent doping with fewer tests
and thereby lower costs by simply differentiating the sanctions. This is
in line with the policy of most sports associations that all winners but
only some losers have to attend a test after the competition. Even if
the verdicts for positively tested winners and losers are identical
(mostly a temporal ban), this hurts the winners much more than the
losers because the former may have to return their prize money and are
very likely to lose most of their lucrative endorsement contracts.

A major shortcoming of the analysis is that the author did not
model the impact of a "windfall-profit effect" (Krakel, 2007)
that arises when the winner prize is awarded to the loser in case the
winner got defaulted due to doping while the loser proved to be clean.
Such a policy is a strong incentive to abstain from doping and to hope
that the competitor dopes instead.(15)

Berentsen and Lengwiler (2004) analyzed evolutionary doping games
with different types of players. Players can be either strong or weak,
with a given probability q, and are matched randomly with either another
strong or another weak player in a contest. If both are strong or both
are weak, then their win probabilities without any doping are 1/2. If a
strong player is matched to a weak one and both are either doped or
clean, the former wins with certainty. If one player, weak or strong, is
doped and the other one is not, the doped one wins with certainty.
Finally, if both players are doped, their win probabilities are
unchanged compared to the situation in which both are clean. Contrary to
most other models, the players in this evolutionary game do not choose
their best possible strategy but are "programmed" to follow a
pure strategy, that is, they are either doping all the time or always
stay clean. As long as one of the two strategies has a higher expected
value than the other one, it proliferates at the expense of that other
strategy. In equilibrium, both strategies have to be equally good or one
will disappear, at least for one type of players. The interesting result
of this model is that anything can happen depending on the parameter
values.(16) There are equilibria where all players are doping; in
others, nobody dopes; and in still others, only the strong or only the
weak athletes take drugs. Finally, there can be cycles in which doping
is used for a while and not at other times. The intuition here is that a
strong player matched with a weak one only wants to dope as long as the
weak one does, who, in turn, is only interested in doping as long as the
strong one stays clean.

Dilger and Tolsdorf (2004, 2005) chose a much simpler and at the
same time very general approach derived from decision theory instead of
game theory.(17) This allowed them to model quite easily the behavior of
a large number of athletes instead of just two. Here, each athlete makes
his decision by taking the behavior of the other contestants as given.
This is not quite correct because the opponents' decisions are not
independent of the individual's decisions (which is, of course,
fully recognized in game-theoretical models). Nevertheless, one can
search for an equilibrium in which the beliefs of all participants are
mutually consistent. As long as game-theoretical models with many
players are too complex to be solved even by the most gifted
economists,(18) professional athletes' behavior may be consistent
with these models as they will have to use simpler heuristics and
therefore find the decision-theoretical one particularly appealing. It
simply lumps together the different factors that influence the utility
of an athlete. That utility will then be maximized taking into account
the potential costs and benefits of doping.

The utility without doping can be written, for example, as
[[mu].sub.nd] = pa + r, where p is the probability of winning, a the
utility from winning, and r is the utility that is derived from being an
athlete who can be either positive (e.g., due to the joy of just doing
it) or negative (e.g., due to the opportunity costs of time). The
utility with doping is [u.sub.d] = (1-[[theta].sub.d])(p + [delta])a +
r-[[theta].sub.d]S-c, where [[theta].sub.d] is the probability that a
doped athlete is detected, [delta] is the higher win probability induced
by doping, S the utility loss, and c is all other costs of doping like
drug prices, health risks. If one is interested in any other effect, for
example, the probability [[theta].sub.nd] that a clean athlete is tested
positive, it is easy to add that to the model. Comparing the utility
levels with and without doping, an athlete will dope if and only if
[[delta].sub.a]-[[theta].sub.d](p+[delta])a - [[theta].sub.d]S-c > 0.
It is simple to derive from this a number of direct effects:(19) more
effective drugs, a higher level of prize money, a lower detection
probability, a lower initial probability of winning, lower sanctions,
and lower doping costs will all increase the probability of doping. This
is also to be expected when competition increases and in case of
athletes who are close to the end of their careers.

In a number of recent articles, alternative mechanisms to deter
doping have been discussed.

* Tietzel and Muller (2000) argued that "negative lists"
including all the substances that are (currently) forbidden exaggerate
the doping problem as they reward the search for and development of new
substances to substitute the forbidden ones. Therefore, they propose a
"fairness-treaty" between sport associations and sponsors as a
potential solution: sport associations and promoters should ban
positively tested athletes forever,(20) while sponsors should pay for
the application and the further development of (better) doping tests.
These suggestions are not very convincing for a number of reasons: if
the recommended treaty was helpful in the fight against doping, it would
have been concluded in the meantime. Moreover, a lifelong ban for one
positive test is problematic as it neglects the possibility of a wrong
test result. Finally, the doping dilemma remains the same irrespective
of whether the state tries to solve it with laws or sport associations
try to do so with voluntary treaties.

* Meannig (2000, 2002) suggested that professional athletes should
pay part of their prize money into a fund. That money will eventually be
paid back to athletes who stayed clean over their careers after they
have retired. Thus, athletes should post bonds that will be forfeited if
they are caught cheating (this is similar to the deferred compensation
model developed by Lazear [1979]). The main advantage of this proposal
is that older athletes at the end of their career can effectively be
deterred from doping because they have more to lose than younger
athletes. This, in turn, is likely to avoid any end-game effects.
Finally, Maennig proposed the introduction of a "positive
list" including drugs that are explicitly allowed. Anything that is
not included in that list would, therefore, be illegal and its use be
punished. Although this will slow down the pace at which new drugs will
be developed, it will certainly lead to an increase in the number of
cases of "unintentional" doping.

* Prinz (2005) questioned whether there is any meaningful
difference between doping and training because in both cases, a
"competition paradox" exists that, in turn, results in a
particular dilemma--a systematic difference between individual and
collective rationality: whether an athlete trains or dopes, he always
produces a negative externality for his opponents. While in the case of
training this is honored by organizers, sponsors, and spectators, this
is most likely not the same in case of doping. However, if the
"gladiator effect" (Prinz, 2005) really exists (fans are
interested only in the winner and not in the way success has been made
possible) and is sufficiently strong, then "the war against
doping" is already lost (and it may, therefore, be legalized).

* Osborne (2005) pointed out that training is very often more
detrimental to an athlete's health than doping and that in many
sports, harming the health of opponents is even the ultimate goal (such
as in boxing). Therefore, the case that has been made against doping so
far is not a very convincing one. He suggested another explanation: fans
not only want to see an excellent athletic performance but also want to
see athletes expending a lot of effort. Doping very often is not only
complementary to effort but also a potential substitute.(21) Thus, fans
want to be able to distinguish between "honest" athletes
working hard and "lazy dopers" able to deliver a possibly even
better performance. If fans expect that athletes replace hard work by
using drugs, their utility and, therefore, their willingness to pay will
be considerably reduced. As a result, athletes as well as sporting
associations have an incentive at least to pretend that the sport is
free of doping.

IV. A REVIEW OF THE (RARE) EMPIRICAL EVIDENCE

Apart from one notable exception, systematic empirical evidence on
the frequencies of doping or its determinants is not yet available. This
is not surprising, given the "illegal" character of using
performance-enhancing drugs. To the best of our knowledge, only two
further studies exist so far that attempt to test some of the
implications derived from the models presented above.

Pitsch, Emrich, and Klein (2005) reported the results of a
www.survey in which they applied the randomized response technique to
elicit information on the prevalence of doping among German elite
athletes. Based on a rather large sample with about 450 respondents,
they found that approximately half of the population had at some stage
of their careers used doping. The percentage of dopers among athletes
competing at the national level is only estimated at 42%, and among
athletes competing at international level, the respective share is 58%.

Dilger and Tolsdorf (2005) used an unbalanced panel of 64
world-class sprinters who participated in 3,024 different 100-m races
during the period 1997-2002. Of these 64 athletes, 16 (25%) have been
tested positively at some stage during these six seasons. Controlling
for a number of other (potential) determinants of individual performance
(such as the importance of the particular event, weather conditions,
stage of the tournament, i.e., heat vs. final),(22) they found that
athletes who have been found cheating participated in a significantly
lower number of races (28 vs. 54) than observationally similar but clean
athletes.(23) Apparently, doped athletes fear detection and, therefore,
enter fewer competitions than their (seemingly) clean colleagues.
Moreover, athletes who have been tested positively are significantly
older (about 3 yr), suggesting that in its present form, the threat of
punishment (athletes are banned for at most 2 yr) leads to a significant
increase in the probability of cheating when athletes reach the end of
their careers.

The standard deviation of athletes' performance is
significantly (at the 1% level) lower if they use illegal drugs (0.171
sec compared to 0.261 sec for clean sprinters). Maintaining a high level
of fitness and being able to repeat an excellent performance are
obviously easier under the influence of "supportive"
medication. Doping seems less helpful in increasing one's potential
than in using it more fully most of the time. Athletes are best in the
season in which they are positively tested. This underlines that doping
really improves the individual's performance. An optimistic
interpretation of this result would be that most athletes are really
clean most of the time and offenders are caught soon. Alternatively, the
positively tested athletes may simply have exaggerated what they and
most others always do (just more carefully). Finally, it may simply
reflect the fact that a better performance increases the probability of
being selected for a doping test.

A second study by Dilger and Tolsdorf (unpublished(24)) uses data
on 187 identified cheaters from professional track and field, who got
caught in the years 1999-2004, among them 7 world record holders, 9
continental record holders, 25 national record holders, 8 Olympic
champions, 16 world champions, 11 continental champions and 14 national
champions. The offenders came from all disciplines: 123 runners (among
them 43 sprinters, 22 middle distance, 26 long distance, and 15 marathon
runners as well 17 hurdle runners), 19 jumpers (among them 7 practicing
pole vault, 6 long and triple jump, and 6 high jump), 39 throwers (among
them 18 practicing shot-put, 7 javelin throw, 7 hammer throw, and 7
discus throw), and, finally, 6 race walkers. The study finds that the
degree of competition (i.e., the "closeness" of the
performance of the best 30 athletes of a particular discipline in a
given year measured by the Gini-coefficient) leads to a significant
increase in the number of positively tested athletes in a discipline.
(25). Although the number of female athletes who have been caught
cheating is considerably lower than the number of men (84 vs. 103),
gender has no significant impact in the model. The reason is that in the
women's contests, the degree of competition is significantly lower.
This together with the significant competition variable implies that
"cutthroat competition" is likely to induce behavior that most
people would consider unacceptable (in accordance with the theory given
in Section III).

More indirect evidence on the frequency of doping can be derived
from studies by Bernard and Busse (2004) and Sterken and Kuper (2003)
who tried to explain the variance in the number of medals won in the
Summer Olympic Games 1960-1996 by the participating nations. Controlling
for country size (log of population). country wealth (log of gross
national product per capita), home advantage (host nation dummy), and
lagged medal share, they found that nations that formerly belonged to
the Soviet bloc were far more successful than expected. This can be
attributed either to the relevance of "state doping" or to a
more "lenient" control system. (26).

Summarizing, it appears that the evidence is compatible with the
sometimes simple, sometimes elaborate economic models discussed at some
length in this article. However, we are far from being able to present
"stylized facts." As in the literature on the economics of
crime, researchers have to rely on statistics that are notoriously
incomplete.

V. SUMMARY AND POLICY IMPLICATIONS

In economic contests in general and in sports tournaments in
particular, monitoring of the actions taken by participants is
imperfect. Therefore, competition is likely to induce not just work
effort (i.e., investing in the development and use of advanced training
methods) but also other choices at the athlete's discretion that
increase his or her success probability (i.e., cheating in the sense of
taking performance-enhancing drugs). The likelihood of doping clearly
depends on the payoffs in the tournament, the probability of cheating
being detected, the number of contestants, and the penalty associated
with being identified as a cheater.

The currently used measures to deter doping are clearly
insufficient: the negative lists that are currently being used by most
sports associations have the undesirable side effect to intensify the
research for and the development of new drugs that enhance performance.
As new substances can go undetected until a test technology has been
developed, developing a positive list that includes only legal drugs
does not solve the problem either: something that cannot be tested for
will, by definition, not be detected. Moreover, such lists are
intellectually unsatisfying as the criteria according to which drugs are
either included or not accepted remain unclear.

The theoretical literature--starting from the assumption that
doping occurs in a prisoners' dilemma situation--suggests that some
kind of an exogenous intervention is required to deter doping. However,
particularly the more elaborate models that have been deveoped recently
show that everything is possible depending on the circumstances:
sometimes all athletes will be doped, sometimes nobody; in some cases,
the stronger athlete has an incentive to cheat, and in others, it is the
weaker athlete; sometimes athletes dope with a probability of 100%, and
in other situations, that probability is (much) lower.

Given the seemingly incompatible predictions that can be derived
from the models, (27) it is not at all surprising that the list of
recommended measures to deter doping is quite long: while the old
literature clearly advocates higher sanctions to deter athletes from
doping, the new models convincingly show that this is not necessarily a
good idea because high sanctions can even increase the use of doping or
drive clean athletes out of the sport. What would certainly reduce the
amount of doping is an increase in the number of tests and further
refinements of the test technologies. (28) Since the costs of testing
most, if not all, athletes are--and will continue to be--prohibitive,
such a scenario is unlikely (by the way, technology that helps mask the
use of illegal drugs is widely available). From a theoretical point,
there are at least two possible solutions to that problem. First, prizes
can simply be confiscated from people found to have cheated and can be
given to the best loser who has been found clean (this is done, e.g., in
the Olympic Games). This has the effect of reducing the amount of
monitoring required to generate an equilibrium in which neither athlete
dopes (cf. Curry and Mongrain, 2005).(29) Second, organizers can ask
losers "to blow the whistle," that is, the winner is only
tested if he or she is accused of cheating by the loser. This will
reduce the frequencies of cheating, is less costly, and leads to strict
Pareto improvement if sanctions for cheating are sufficiently large
(Berentsen, Brugger, and Lortscher, 2003). (30)

Unfortunately, neither of the two strategies is likely to solve the
problem (completely): since the available test technologies are far from
being perfect (sometimes clean athletes are tested positive and
sometimes doped athletes will go undetected), variations in the
parameters mentioned above--doping costs, detection probability, prize
money, number of contestants, and penalties for cheaters--will at best
reduce but certainly not eradicate illegal activities in sport, once
considered a domain of fairness and integrity.

REFERENCES

Andrews, J. "Superhuman Heroes: Does the End Justify the
Means?" Economist, Survey: The World of Sport, 4th June 1998, 10-4.

Sterken, E., and G. Kuper. "Olympic Participation and
Performance since 1896," in The Economics, the Management and the
Marketing of Sports, edited by G. T. Papanikos. Athens, Greece: Athens
Institute for Education and Research, 2003, 111-130.

(1.) In general, doping is a problem in sports precisely because it
cannot perfectly be verified. Nevertheless, contestants can often
observe it more easily, while outsiders usually lack the ability to
prove it to third parties.

(2.) This assumption has been heavily disputed in the past. It is,
of course, also possible that organizers as well as fans want to see
spectacular performances regardless of how these performances have been
made possible. However, issues such as closeness of the competition,
fairness, or elegance matter empirically. For fans as well as for
sponsors, performance within given constraints seems important, not
absolute performance as such (Konarad, 2005, p. 11).

(3.) These reactions are not unique to Europe: according to a
recent opinion poll conducted by USA Today, more than 86% of American
baseball fans claim that compulsory testing for steroids would renew
their interest in baseball (Curry and Mongrain, 2005, pp. 20-21).

(4.) The amount of caffeine that may be consumed by an athlete
prior to a competition was limited until 2005.

(5.) We deliberately disregard sports like weightlifting, for
example, where recently complete national teams have been sent home from
the World Championships because the majority of the athletes Tailed drug
testing immediately before the opening ceremony. Moreover, we also
disregard sports that are less physical and/or more technical in which
doping is less useful.

(6.) Moreover, baseball players like Barry Bonds and Jason Giambi
as well as several players oi' [he Oakland Raiders were also
involved.

(7.) A convincing definition of the term doping seems to be more of
a technical or even linguistic problem, whereas the forth issue, why
doping is strictly forbidden, is considered a normative
question--something that economists either like to evade or to take the
answer(s) given by philosophers or politicians for granted.

(8.) Sec also Keck (1987). Moreover, Keck and Wagner (1990) argued
that the prisoners' dilemma is not only confined to the individual
athletes but can also be applied to explain the behavior of officials
and national sports associations--with the crucial difference that the
latter will not be punished if doping is detected.

(9.) Maennig (2000) explicitly mentioned only a possible loss of
honor and financial losses resulting from a ban as costs of doping.
Other costs are the negative externalities arising from doping, that is.
the loss of credibility for other athletes. However, all these costs
other than health problems would disappear as soon as doping was
legalized.

(10.) Alas, the difficulty in verifying the illegal use of
substances and procedures remains the same, only the definition of
doping would be clearer.

(11.) Haugen (2004, p. 71) assumed "--for simplistic
reasons--that the payoff received by any agent is kept even if this
agent is caught in doping." This is unnecessary because c could
include a, that is, the costs in case of being caught include the
repayment, although this contradicts the supposition of Haugen (2004,
pp. 72-74) that a is much higher than c since the financial rewards in
professional sports are very high and rising, whereas periods of
exclusion for caught dopers are falling and that when the typical
punishment involves exclusion, there is no history of direct negative
economic consequences. In any case, more problematic is the payoff of
zero for the nondoped athlete because he or she would get some prize,
eventually lower than a, if the doped athlete is caught. Eber and Thepot
(1999) presented a model where the prize of a doped winner is given to
the loser. They also modeled risk aversion and their main conclusion was
that a low spread between the prize for the winner and the loser is the
best remedy against doping.

(12.) It is questionable whether the expected costs are really the
same for both athletes independently of winning. A winner has a higher
chance of being tested than a loser and has probably more to lose by
being detected. Nevertheless, this detail does not change the main
result.

(13.) This is explicitly acknowledged by Haugen (2004, p. 69), who
aimed at "a less technical presentation and. consequently, a
potentially broader audience."

(14.) The intuition behind this counterintuitive result is that
[[delta].sub.2] has to be much larger than [[delta].sub.1], otherwise
both conditions cannot be fulfilled at the same time. More effective
doping for the less talented player means the more talented one dopes
more often to counter this effect, but there remains a disadvantage due
to the mere possibility of asymmetrically effective doping.

(15.) See also Eber and Thepot (1999) and Krakel (2007).

(16.) It is an open empirical question whether these many
possibilities reflect reality or whether the approach developed here
offers few insights for the understanding of doping particularly because
of the large number of possible outcomes.

(17.) Bourg (2000) and Maennig (2002) have first introduced such
models following Becker (1968) in his famous analysis of criminal
behavior.

(18.) This depends on the kind of model, of course. It holds for
most models presented here, but see Bird and Wagner (1997) for an
exception.

(19.) There can be indirect countereffects from the reactions of
others that only a game-theoretical approach is able to identify
systematically. However, the higher the number of (not too
heterogeneous) contestants, the smaller the impact of any individual
athlete, thereby reducing the inaccuracy of a decision-theoretical
approach.

(20.) Buch (2001) also proposed the introduction of the title
"doping-free athlete" as a kind of marketing tool. However,
this may result in even more hypocrisy.

(21.) Konrad (2003) showed doping to be welfare enhancing under the
assumption that it is a complement to other legal inputs. Krkel (2007)
also analyzed the combination of doping and other inputs like training,
which can result in enhanced welfare by doping.

(22.) Most of these control variables are not statistically
significant. The importance of the race, the stage of the tournament,
and the weight and height of the athlete all proved to be irrelevant in
the estimations. However, older sprinters are significantly better than
younger athletes (which might be due to a selection effect).

(23.) The assumption that those who have not been tested positively
are always "clean" is, of course, problematic. Carl Lewis, who
was awarded the gold medal in the 100-m dash in the 1988 Olympic Games
after the suspension of Ben Johnson, later admitted that he had also
been taking drugs during that time. Lewis, however, was never tested
positively.

(24.) For a first sketch with a smaller data set and other
desiderata, see Dilger and Tolsdorf (2004. pp. 274-278).

(25.) The study further controls for fan demand by taking into
account differences in TV ratings during the last World Championships
and Olympic Games and for a linear time trend. These variables as well
as the age of the athletes arc not statistically significant.

(26.) Another explanation emphasizes the importance of sport
funding: if more resources and effort have been expended for high-level
sports in these countries, their performance in the medal counts would
not be too surprising. However, the evidence found after the collapse of
the German Democratic Republic suggests that systematic doping and
doping research did exist at least in that socialist country.

(27.) Summarizing, the game-theoretic models that have been
developed recently to explain the (seemingly widespread) use of doping
(thus mainly addressing Questions 2 and 3 given above) differ in a
number of assumptions: first, are contestants homogenous with regards to
their abilities and the degree of risk-aversion or are they
heterogeneous? Second, do contestants move simultaneously or
sequentially? Third, do contestants benefit from doping to the same
extent or do they react differently to the consumption of banned
substances?

(28.) A simple, yet unrealistic solution to the doping problem is
to reduce the amounts of money that can be earned by the most successful
athletes: with less money at stake, the incentives to use illegal drugs
would be considerably reduced at least for athletes who have exit
options that are acceptable to them. For athletes without exit options,
that is, particularly those from underdeveloped countries whose
second-best alternative is unemployment, such a reduction would also
lead to a change in behavior: if the number of contestants goes down,
the incentives to use illegal drugs go down too.

(29.) Awarding additional prizes to those finishing, for example,
second and third in a tournament has been shown to positively influenec
effort levels by all participants (cf. Valletti and Szymanski, 2005).
This may also help reduce cheating by avoiding a "winner-take-all
contest."

(30.) This approach may be ethically questionable because it relies
on suspicion and informing, contrary to fair play, like doping itself.
It is also based on the assumption that the loser has better knowledge
of doping by the winner than third parties.

* We are grateful to two anonymous referees, whose comments have
considerably improved the article. Any remaining errors and omissions
are, of course, our own.